Generally not. Just as you “can’t take it with you” you just can’t make others responsible for your general debts, at least without their consent. (Otherwise a person could run up lots of debts, name his worst enemy as his beneficiary, and saddle his enemy with those debts at his or her death.)
Unless the deceased had gifted away his or her assets to someone shortly before dying, or otherwise acted in concert with them to defraud his or her creditors, beneficiaries should not have any liability to the deceased’s creditors just because they are beneficiaries. Of course, the Estate may not have anything left for them, but the beneficiaries would not be in the hole.
Of course, if the children or beneficiaries took any property or benefits from the deceased or the estate or had assumed liability for care given the deceased, or guaranteed payment, they could be held liable for some or all of the deceased’s debts separately, not because they are relatives or beneficiaries.
